Am I understanding your post correctly? You're saying that when you are looking at the lock screen, you're able to swipe down to the notification center, tap all settings, and then the start screen button, it's not asking for your password?
While looking at the lock screen, when you swipe up to view the start screen, does it ask for a password to unlock the phone? This can be turned on or off at the very bottom of the lock screen setting after you get to all settings page.
When the lock screen password is on, you are allowed to see the notification center, but it will not allow you to go to the all settings page without entering your password.